2014/02/24 by Hakima Bessaih, Erika Hausenblas, Bessaih, Hakima +4
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.1402.5772
Submitted for publication. Minor correction (typos) have been made. This paper is about strong (more regular in space!) solution of some hydrodynamic equations driven by Levy noise. We use abstract framework as in arXiv:0807.1810 and the examples we took are borrowed from arXiv:0807.1810 which is acknowledged in our text
openalex publication_date 2014/02/24 · arxiv created 2014/07/22 · arxiv updated 2014/07/23 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
In this paper we prove the existence and uniqueness of maximal strong (in PDE sense) solution to several stochastic hydrodynamical systems on unbounded and bounded domains of ℝn, n=2,3. This maximal solution turns out to be a global one in the case of 2D stochastic hydrodynamical systems. Our framework is general in the sense that it allows us to solve the Navier-Stokes equations, MHD equations, Magnetic Bénard problems, Boussinesq model of the Bénard convection, Shell models of turbulence and the Leray-α model with jump type perturbation. Our goal is achieved by proving general results about the existence of maximal and global solution to an abstract stochastic partial differential equations with locally Lipschitz continuous coefficients. The method of the proofs are based on some truncation and fixed point methods.